Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

How would you simplify the expression b^-7/b^-8?

1. b^-7 + 8

2. b^-7 - (-8)

3. b^-7 - 8

4. b^-7 + (-8)

The correct answer is: b^-7 - (-8)

To simplify the expression \( \frac{b^{-7}}{b^{-8}} \), we can use the property of exponents which states that when we divide two powers with the same base, we subtract the exponents. In this case, we have: \[ \frac{b^{-7}}{b^{-8}} = b^{-7 - (-8)} = b^{-7 + 8} = b^{1} \] This means the expression simplifies to \( b^{1} \), which is simply \( b \). The calculation shows that the exponent on the bottom was subtracted, but since it was negative, we actually added it when subtracting the exponent. So, the correct method involves recognizing that the operation with the exponents can be handled by combining them, resulting in the expression \( b^{1} \). The choice that reflects this operation accurately is the one that conveys the idea of \( -7 + 8 \).